Spectroscopy ofMg20: The isobaric mass multiplet equation for the2+states of theA=20,T=2quintet and distant mirror nuclei

Abstract

We report on the first determination of the ${2}_{1}^{+}$ energy of $^{20}\mathrm{Mg}$, the most neutron-deficient Mg isotope known to exist. The result, $E({2}_{1}^{+})=1598(10)$ keV, obtained from in-beam \ensuremath{\gamma}-ray spectroscopy following the two-neutron removal from a $^{22}\mathrm{Mg}$ secondary beam, is discussed in the framework of the isobaric mass multiplet equation (IMME). Resulting predictions for the excitation energies of the $T=2,{2}^{+}$ states in the $^{20}\mathrm{F}$ and $^{20}\mathrm{Na}$ isobars are presented. The mirror energy difference, $E({2}_{1}^{+},$$^{20}\mathrm{Mg}$$)\ensuremath{-}E({2}_{1}^{+},$$^{20}\mathrm{O}$$)=\ensuremath{-}77(10)$ keV, is compared to a recent prediction within the nuclear shell model based on the ``${\mathrm{USD}}^{m}$ - gap Z14'' modification of the universal $\mathit{sd}$ (USD) effective interaction.